Place 1/2 the peaches in a large saucepan and crush until mostly mashed. Add the remaining peaches and mangos. Bring to a boil over medium-low heat. Cook until mostly liquid, 20 to 30 minutes.
Pour peach-mango mixture into a bowl and measure 5 1/4 cups back into the pan. For a thicker mixture, use only 5 cups. Add sugar to the pan and bring to a boil over medium heat. Gradually stir in pectin and bring back to a boil. Boil for 1 minute; immediately remove from heat.
Pour preserves into hot, sterilized jars, filling to within 1/4 inch of the top. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any residue. Top with lids and screw on rings.
Place a rack in the bottom of a large canning pot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 5 minutes.